Data-Refinement for Call-By-Value Programming Languages

Kinoshita, Yoshiki; Power, John

doi:10.1007/3-540-48168-0_39

Cited by 16 publications

(22 citation statements)

References 8 publications

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“…However, the main topic of this paper is a more complex situation of lax logical relations and data-refinement for the computational lambda calculus. A subsequent paper (Power and Tanaka, 2000) develops further the ideas of (Kinoshita and Power, 1999). It addresses in particular lax logical relations for the computational lambda calculus and for the linear lambda calculus.…”

Section: Related Workmentioning

confidence: 99%

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Logical Relations for Monadic Types

Goubault-Larrecq

Lasota

Nowak

2002

Computer Science Logic

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Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi's computational lambda-calculus. The treatment is categorical, and is based on notions of subsconing, mono factorization systems, and monad morphisms. Our approach has a number of interesting applications, including cases for lambda-calculi with non-determinism (where being in logical relation means being bisimilar), dynamic name creation, and probabilistic systems.

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Section: Related Workmentioning

confidence: 99%

“…(Kinoshita and Power, 1999) consider lifting a monad on Set Set Set to the category of relations in Set Set Set. This is a particular case of our setting.…”

Section: Related Workmentioning

confidence: 99%

Logical Relations for Monadic Types

Goubault-Larrecq

Lasota

Nowak

2002

Computer Science Logic

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“…It would be straightforward to generalise our analysis to include such possibilities, but it may be simpler to deal with them case by case. For an analysis of the notion of lax logical relations where contexts are modelled by a Freyd structure, see [KP99].…”

Section: Proposition 72 Binary Lax Logical Relations (At the Currenmentioning

confidence: 99%

Lax Logical Relations

Plotkin

Power

Sannella

et al. 2000

Automata, Languages and Programming

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Abstract. Lax logical relations are a categorical generalisation of logical relations; though they preserve product types, they need not preserve exponential types. But, like logical relations, they are preserved by the meanings of all lambda-calculus terms. We show that lax logical relations coincide with the correspondences of Schoett, the algebraic relations of Mitchell and the pre-logical relations of Honsell and Sannella on Henkin models, but also generalise naturally to models in cartesian closed categories and to richer languages.

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“…Over recent years, there has been a concerted attempt, led by Gordon Plotkin and myself, to develop a unified, elegant theory of computational effects, with both operational and denotational semantics, a logic, and theorems relating them, designed to analyse and reason about call-by-value functional programming languages that extend the simply typed λ-calculus, along the lines of ML [4,5,6,7,13,14,15,16,17]. Our starting point has typically been Eugenio Moggi's computational λ-calculus or λ c -calculus, which was introduced in [10,11], with four distinct sound and complete classes of category theoretic models explained in [18], and with further abstract semantic development in [8,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

Canonical Models for Computational Effects

Power

2004

Lecture Notes in Computer Science

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Abstract. Given a signature of basic operations for a computational effect such as side-effects, interactive input/output, or exceptions, we give a unified construction that determines equations that should hold between derived operations of the same arity. We then show how to construct a canonical model for the signature, together with the firstorder fragment of the computational λ-calculus, subject to the equations, done at the level of generality of an arbitrary computational effect. We prove a universality theorem that characterises the canonical model, and we recall, from a previous paper, how to extend such models to the full computational λ-calculus. Our leading example is that of side-effects, with occasional reference to interactive input/output, exceptions, and nondeterminism.

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Data-Refinement for Call-By-Value Programming Languages

Cited by 16 publications

References 8 publications

Logical Relations for Monadic Types

Logical Relations for Monadic Types

Lax Logical Relations

Canonical Models for Computational Effects

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